Some new closed-form solutions describing spherical inflation in compressible finite elasticity

Within the context of finite elasticity, considerable interest has been shown in the problem of inflating spherical shells of special compressible materials. Three new closed-form solutions to the above problem are presented. The qualitative features of the inflation of thin shells of these special materials are then studied. The related problems of spherical eversion and cylindrical inflation are also briefly considered. The problem of spherical inflation and compaction of shells of special compres-sible materials has been studied in a number of recent papers. For the harmonic material introduced by John [1], a closed-form solution to the equations of equilibrium describing spherical inflation and compaction was presented b